Liviu Nicolaescu's An Invitation to Morse Theory (Universitext) PDF

This self-contained remedy of Morse thought specializes in purposes and is meant for a graduate path on differential or algebraic topology. The e-book is split into 3 conceptually unique elements. the 1st half comprises the principles of Morse thought (over the reals). the second one half involves purposes of Morse concept over the reals, whereas the final half describes the fundamentals and a few purposes of advanced Morse thought, a.k.a. Picard-Lefschetz theory.This is the 1st textbook to incorporate issues equivalent to Morse-Smale flows, min-max concept, second maps and equivariant cohomology, and intricate Morse conception. The exposition is improved with examples, difficulties, and illustrations, and may be of curiosity to graduate scholars in addition to researchers. The reader is anticipated to have a few familiarity with cohomology idea and with the differential and vital calculus on tender manifolds.Liviu Nicolaescu is affiliate Professor of arithmetic at collage of Notre Dame.

Articles learn the contributions of the good mathematician J. M. Hoene-Wronski. even though a lot of his paintings used to be disregarded in the course of his lifetime, it truly is now famous that his paintings bargains worthwhile perception into the character of arithmetic. The booklet starts with elementary-level discussions and ends with discussions of present examine.

This e-book is an creation to singularities for graduate scholars and researchers. it truly is acknowledged that algebraic geometry originated within the 17th century with the well-known paintings Discours de los angeles méthode pour bien conduire sa raison, et chercher los angeles vérité dans les sciences via Descartes. In that publication he brought coordinates to the examine of geometry.

This booklet is an advent to trendy equipment of symplectic topology. it really is dedicated to explaining the answer of a tremendous challenge originating from classical mechanics: the 'Arnold conjecture', which asserts that the variety of 1-periodic trajectories of a non-degenerate Hamiltonian method is bounded lower than via the size of the homology of the underlying manifold.